Character physics "jump limit" in bge....!
There is no easy way to do this. Even though there is a jumpCount property you can not edit it via script as it's readable only. However, after some tests I found a hacky workaround that might do it for you, because resetting the gravity seems to reset the jumpCounter. It can by achieved by this procedure:

Paste this script into the text editor.

import bge

def main():
    cont = bge.logic.getCurrentController()
    own = cont.owner
    hero = bge.constraints.getCharacter(own)
    hero.jump()

    # Reset the gravity:
    hero.gravity = 0
    hero.gravity = 30 #default value. You might change this :)
main()


Then use the following setup on your player to trigger the script. Notice that the jumping is also done via the script.